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CLEP College Math Topics

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1Adding and Subtracting Integers

1.1Introduction to integer addition
1.2Adding integers
1.3Introduction to integer subtraction
1.4Subtracting integers
1.5Application of integer operations

2Multiplying and Dividing Integers

2.1Multiplying integers
2.2Dividing integers

3Primes and Common Factors

3.1Prime factorization
3.2Least Common Multiple (LCM) (free lessons)
3.3Greatest Common Factors (GCF)

4Fractions

4.1Adding fractions with like denominators
4.2Subtracting fractions with like denominators
4.3Adding and subtracting fractions with unlike denominators
4.4Multiplying proper fractions
4.5Dividing fractions and mixed numbers

5Decimals

5.1Adding and subtracting decimals
5.2Multiplying decimals
5.3Dividing decimals
5.4Order of operations (BEDMAS)
5.5Scientific notation
5.6Rational vs. Irrational numbers

6Expressions and Equations

6.1Patterns
6.2Adding and subtracting polynomials
6.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
6.4Multiplying polynomials by monomials
6.5Solving linear equations using multiplication and division (free lessons)
6.6Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
6.7Solving one - step equations: x+a=bx + a = b
6.8Solving linear equations with variables on both sides

7Introduction to Equations

7.1Evaluating algebraic expressions
7.2Solving literal equations
7.3Applications of polynomial functions
7.4Money related questions in linear equations (free lessons)

8Absolute Value Equations

8.1Absolute value functions (free lessons)
8.2Solving absolute value equations
8.3Solving absolute value inequalities

9Graphing Inequalities

9.1Express linear inequalities graphically and algebraically (free lessons)
9.2Solving one-step linear inequalities (free lessons)
9.3Solving multi-step linear inequalities (free lessons)
9.4Graphing linear inequalities in two variables (free lessons)

10Linear Equations

10.1Word problems of graphing linear functions
10.2Rate of change
10.3Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
10.4Graphing linear functions using a single point and slope
10.5General form: Ax + By + C = 0 (free lessons)
10.6Point-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
10.7Parallel and perpendicular lines in linear functions (free lessons)

11Graphing Functions

11.1Domain and range of a function (free lessons)
11.2Identifying functions
11.3Function notation (free lessons)
11.4Graphing linear functions using table of values
11.5Graphing from slope-intercept form y=mx+b
11.6Graphing linear functions using x- and y-intercepts (free lessons)
11.7Using elimination method to solve systems of equations
11.8Using substitution method to solve systems of equations

12Exponents and Multiplying Polynomials

12.1Direct variation
12.2Multiplying binomial by binomial (free lessons)

13Factoring

13.1Common factors of polynomials (free lessons)
13.2Factor by taking out the greatest common factor (free lessons)
13.3Factoring polynomials: ax2+bx+cax^2 + bx + c
13.4Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
13.5Factoring difference of squares: x2−y2x^2 - y^2
13.6Introduction to quadratic functions (free lessons)

14Radical Expressions and Quadratic Equations

14.1Evaluating and simplifying radicals
14.2Converting radicals to mixed radicals
14.3Solving quadratic equations by factoring
14.4Solving quadratic equations by completing the square
14.5Using quadratic formula to solve quadratic equations
14.6Transformations of quadratic functions

15Introduction to Geometry

15.1Cartesian plane
15.2Parallel and perpendicular line segments
15.3Horizontal and vertical distances

16Statistics

16.1Reading and drawing bar graphs
16.2Reading and drawing line graphs
16.3Circle graphs
16.4Reading and drawing histograms
16.5Box-and-whisker plots and scatter plots
16.6Median and mode
16.7Mean
16.8Application of averages

17Probability

17.1Introduction to probability
17.2Organizing outcomes
17.3Probability of independent events
17.4Comparing experimental and theoretical probability

18Angle Pair, Parallel, and Perpendicular Lines

18.1Parallel line proofs
18.2Perpendicular line proofs (free lessons)
18.3Inscribed Angles and Proofs
18.4Standard angles
18.5Coterminal angles (free lessons)
18.6Reference angles

19Triangles

19.1Classifying Triangles
19.2Congruence and Congruent Triangles
19.3Triangles Congruent by SSS Proofs
19.4Triangles Congruent by SAS and HL Proofs
19.5Triangles Congruent by ASA and AAS Proofs
19.6Isosceles and Equilateral Triangles

20Relations in Triangles

20.1Unit circle (free lessons)
20.2Law of sines
20.3Law of cosines
20.4Applications of the sine law and cosine law

21Ratio, Proportion, Similarity, & Percent

21.1Ratios (free lessons)
21.2Similar polygons
21.3Percents, fractions, and decimals
21.4Percent of a number
21.5Pythagorean theorem (free lessons)
21.6Applications of pythagorean theorem
21.7Solving expressions using 30-60-90 special right triangles
21.8Solving expressions using 45-45-90 special right triangles (free lessons)

22Right Triangles

22.1Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h} ) (free lessons)
22.2Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h} )
22.3Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )
22.4Other word problems relating angles in trigonometry

23Beginning Measurement

23.1Metric systems (free lessons)
23.2Imperial systems
23.3Conversions between metric and imperial systems
23.4Conversions involve squares and cubic

24Circles

24.1Tangent properties
24.2Circle and circumference
24.3Arcs of a circle
24.4Areas and sectors of circles
24.5Central and inscribed angles in circles

25Surface Area and Volume

25.1Surface area and volume of prisms (free lessons)
25.2Surface area and volume of pyramids
25.3Surface area and volume of cylinders
25.4Surface area and volume of cones (free lessons)
25.5Surface area and volume of spheres

26Coordinate Geometry

26.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
26.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
26.3Solving second degree trigonometric equations

27Negative and Rational Exponents

27.1Exponents: Negative exponents
27.2Combining the exponent rules
27.3Rational exponents
27.4Solving radical equations
27.5Basic radical functions

28Composite Functions and Inverses

28.1Composite functions (free lessons)
28.2Inverse functions (free lessons)

29Logarithms and Exponential Functions

29.1What is a logarithm?
29.2Evaluating logarithms without a calculator
29.3Product rule of logarithms (free lessons)
29.4Quotient rule of logarithms
29.5Combining product rule and quotient rule in logarithms
29.6Solving logarithmic equations (free lessons)
29.7Evaluating logarithms using change-of-base formula
29.8Exponential growth and decay by a factor
29.9Exponential decay: Half-life (free lessons)
29.10Natural log: ln
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